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physica status solidi (b)

Phonoritons and Energy Spectrum Instabilities of the Exciton-Photon-Phonon System

E. S. Kiselyova, S. A. Moskalenko

Published Feb 1, 1999• 2 citations
Publisher

Abstract

The energy spectrum of the elementary excitations arising in the three-component exciton–photon–phonon system in the presence of a macroscopic large coherent exciton mode is considered, supposing the Bose-Einstein condensation of excitons on the single particle state with wave vector k = 0. The Green's functions describing the system in the frame of the Belyaev diagram technique obey to a set of Dyson equations. There are three initial branches of the noninteracting subsystems. They have the form of the Bogolyubov type excitonic spectrum, phonon branch and photon spectrum counted from the chemical potential value. In the six points of their intersections a strong reconstruction of the spectrum takes place. In three of them the spectrum is stable. Here simple and evanescent waves can exist. In the other three points of intersections absolute or nonconvective instabilities of the spectrum appear.

DOI
10.1002/(sici)1521-3951(199902)211:2<693::aid-pssb693>3.0.co;2-6

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The energy spectrum of the elementary excitations arising in the three-component exciton–photon–phonon system in the presence of a macroscopic large coherent exciton mode is considered, supposing the Bose-Einstein condensation of excitons on the single particle state with wave vector k = 0. The Green's functions describing the system in the frame of the Belyaev diagram technique obey to a set of Dyson equations. There are three initial branches of the noninteracting subsystems. They have the form of the Bogolyubov type excitonic spectrum, phonon branch and photon spectrum counted from the chemical potential value. In the six points of their intersections a strong reconstruction of the spectrum takes place. In three of them the spectrum is stable. Here simple and evanescent waves can exist. In the other three points of intersections absolute or nonconvective instabilities of the spectrum appear.
The system under consideration is a multicomponent gas of interacting paraexcitons and orthoexcitons confined in a three-dimensional potential trap. We calculate the spatially resolved optical emission spectrum due to interband transitions involving weak direct and phonon-mediated exciton-photon interactions. For each component, the occurrence of a Bose-Einstein condensate changes the spectrum in a characteristic way so that it directly reflects the constant chemical potential of the excitons and the renormalization of the quasiparticle excitation spectrum. Moreover, the interaction between the components leads, in dependence on temperature and particle number, to modifications of the spectra indicating phase separation of the subsystems. Typical examples of density profiles and luminescence spectra of ground-state paraexcitons and orthoexcitons in Cu2O{\text{Cu}}_{2}\text{O}Cu2​O are given.
We examine the absorption and amplification bands of a weak probe signal in the presence of Bose-Einstein condensation of excitons that emerges in nonequilibrium conditions in the field of coherent laser radiation with a wave vector k 0. We assume that the detuning Δ~\tilde \Delta Δ~ from resonance between the energy ħω ex (k 0)+L 0 of the exciton level, which is shifted because of exciton-exciton interaction, and the laser photon energy ħω L , is generally nonzero. The elementary excitation spectrum consisting of the quasiexcitonic and quasienergy branches determines the optical properties of the system. When there is real induced Bose-Einstein condensation, at Δ~=0\tilde \Delta = 0Δ~=0 the two branches touch, as they do in spontaneous Bose-Einstein condensation. In virtual induced Bose-Einstein condensation, when Δ~<0\tilde \Delta < 0Δ~<0 , instabilities emerge in the spectrum in certain regions of the k-space. These instabilities are caused by a real transformation of two laser photons into two extracondensate particles. Nonequilibrium extracondensate excitons strongly affect the absorption and amplification of the probe light signal. We show that light absorption is due to the quantum transition from the ground state of the crystal to the quasiexcitonic branch of the spectrum. On the other hand, amplification of the signal is caused by the transition from the quasienergy branch to the ground state of the crystal. The same transition can be explained by a real transformation of two laser photons into a vacuum photon of frequency ħcq and a crystal exciton with a wave vector 2k 0−q. Finally, we show that the excitonic absorption and light-amplification bands are essentially anisotropic at Δ~≈0\tilde \Delta \approx 0Δ~≈0 and depend on the orientation of the vectors q and k 0.
The elementary excitation spectrum of a two-component Bose—Einstein condensate in different hyperfine states is obtained by Green's function method. It is found to have two branches. In the long wave-length limit, the two branches of the excitation spectrum are reduced to one phonon excitation and one single-particle excitation. The single-particle one has an energy gap. When the energy gap exists, we study the Landau critical velocity and the depletion of the condensate. With the obtained Green's functions, we calculate the structure factor of a two-component condensate. It is found that the static structure factor comprises only the branch of the phonon excitation and the single-particle excitation makes no contribution to the structure factor.
The spectrum of phonon-like collective excitations in the system of Bose-atoms in optical lattice (more generally, in the system of quantum particles described by the Bose-Hubbard model) is investigated.Such excitations appear due to displacements of particles with respect to their local equilibrium positions.The two-level model taking into account the transitions of bosons between the ground state and the first excited state in potential wells, as well as interaction between them, is used.Calculations are performed within the random phase approximation in the hard-core boson limit.It is shown that excitation spectrum in normal phase consists of the one exciton-like band, while in the phase with BE condensate an additional band appears.The positions, spectral weights and widths of bands strongly depend on chemical potential of bosons and temperature.The conditions of stability of a system with respect to the lowering of symmetry and displacement modulation are discussed.
The exciton absorption and emission bands in the presence of Bose-Einstein condensation (BEC) of excitons, induced by the coherent laser radiation is considered. The laser radiation creates the coherent macroscopic polarization of the crystal, which is described as a virtual BEC of excitons. The energy spectrum of the elementary excitations as well as the probabilities of the quantum transitions depend essentially on the frequency detuning (Delta) -. The nonequilibrium occupation numbers of out-of-condensate excitons nexq arising in the presence of virtual BEC influence on the forms of absorption and emission bands.